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2-DIMENSIONAL CELLULAR AUTOMATA
The Computational Universe
2006 NKS ConferenceMichael Round
USA Director: Theory of Constraints for Education
INTUITIVE UNDERSTANDING of RULES
A Necessary Condition for NKS-Excellence …
1 1 0 1 1 0 1
0 1 0 1 0 0 1 0
1 0 1 1 0 1
rule 101
0 0 0 0 0 0 0
rule 000 0 0 0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0 0
rule 001 0 1 0 1 0 0 1 0
0 0 0 0 0 0
0 0 1 0 0 1 0
rule 010 1 0 1 0 1 1 0 1
0 1 0 0 1 0
0 0 1 0 0 1 0
rule 011 1 1 1 1 1 1 1 1
0 1 0 0 1 0
1 1 0 1 1 0 1
rule 100 0 0 0 0 0 0 0 0
1 0 1 1 0 1
1 1 0 1 1 0 1
rule 101 0 1 0 1 0 0 1 0
1 0 1 1 0 1
1 1 1 1 1 1 1
rule 110 1 0 1 0 1 1 0 1
1 1 1 1 1 1
1 1 1 1 1 1 1
rule 111 1 1 1 1 1 1 1 1
1 1 1 1 1 1
INTUITIVE UNDERSTANDING of RULES
… demonstrating “Intrinsic Beauty”
Grid Number Unique Total 2-D
Columns Cells "Cartesian Snowflakes"
1 1 2
2 3 8
3 6 64
4 10 1,024
5 15 32,768
6 21 2,097,152
7 28 268,435,456
8 36 68,719,476,736
9 45 35,184,372,088,832
10 55 36,028,797,018,964,000
11 66 73,786,976,294,838,200,000
12 78 302,231,454,903,657,000,000,000
13 91 2,475,880,078,570,760,000,000,000,000
INTUITIVE UNDERSTANDING of 2-D CA RULES as PROCESSES
Seeing the Rule from Decimal to Binary
initial conditionsany 8 any 7 any 6 any 5 any 4 any 3 any 2 any 1 zero
5-neighbor outer totalistic cellular automaton: rule 494 iteration 40
5
000000000111101110
neighbors?include self?
decimal:binary:
yes494
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64
65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88
89 90 91 92 93 94 95 96
97 98 99 100 101 102 103 104
105 106 107 108 109 110 111 112
113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128
129 130 131 132 133 134 135 136
137 138 139 140 141 142 143 144
145 146 147 148 149 150 151 152
153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168
169 170 171 172 173 174 175 176
177 178 179 180 181 182 183 184
185 186 187 188 189 190 191 192
193 194 195 196 197 198 199 200
201 202 203 204 205 206 207 208
209 210 211 212 213 214 215 216
217 218 219 220 221 222 223 224
225 226 227 228 229 230 231 232
233 234 235 236 237 238 239 240
241 242 243 244 245 246 247 248
249 250 251 252 253 254 255 256
257 258 259 260 261 262 263 264
265 266 267 268 269 270 271 272
273 274 275 276 277 278 279 280
INTEGRATING PHYSICAL SCIENCE into 2d-CA
The Nature of the Water Molecule
INTEGRATING PHYSICAL SCIENCE into 2d-CA
A Classification System of the Operation of Water Molecules in a System
INTEGRATING PHYSICAL SCIENCE into 2d-CA
The Operation of Water Molecules in a System
INTEGRATING PHYSICAL SCIENCE into 2d-CA
Integrating “Computation” into the Understanding of a System
141516
DESIRABLE EFFECTS on IMPLEMENTATION
“Joy in Learning” of the Computational Universe
Rules and processes are easily and intuitively
understood.
K-12 kids will enjoy computational
experimentation.
There is integration of science and the world
in these materials.
The K-12 learning environment can think
of the world “computationally”.
initial conditionsany 8 any 7 any 6 any 5 any 4 any 3 any 2 any 1 zero
236 is odd
5
000000000000000000
neighbors?include self?
decimal:binary:
yes
5-neighbor outer totalistic cellular automaton: rule iteration 40
initial conditions:
2=random matrix3=random with symmetry4=manual
1=simple 3
1 1
00
1 1 110
0 111
101 1
10
1 00
0 0 1 1 1 0 0
1
1 1 01 1 01 1 0 1 1
1 0 0 1 0 0 1
track growth
reset
reset start activate start
view growth
track simulations (same rule)
track rules
